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ОбложкаHillert M. Phase equilibria, phase diagrams and phase transformations: their thermodynamic basis. - 2nd ed. - Cambridge; New York: Cambridge University Press, 2008 (2009). - xiv, 510 p.: ill. - Ref.: p.496-497. - Ind.: p.499-510. - ISBN 978-0-521-85351-4
Шифр: (И/В31-Н66) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
 
   Preface to second edition .................................. xii
   Preface to first edition .................................. xiii

1  Basic concepts of thermodynamics ............................. 1
   1.1  External state variables ................................ 1
   1.2  Internal state variables ................................ 3
   1.3  The first law of thermodynamics ......................... 5
   1.4  Freezing-in conditions .................................. 9
   1.5  Reversible and irreversible processes .................. 10
   1.6  Second law of thermodynamics ........................... 13
   1.7  Condition of internal equilibrium ...................... 17
   1.8  Driving force .......................................... 19
   1.9  Combined first and second law .......................... 21
   1.10 General conditions of equilibrium ...................... 23
   1.11 Characteristic state functions ......................... 24
   1.12 Entropy ................................................ 26
2  Manipulation of thermodynamic quantities .................... 30
   2.1  Evaluation of one characteristic state function from
        another ................................................ 30
   2.2  Internal variables at equilibrium ...................... 31
   2.3  Equations of state ..................................... 33
   2.4  Experimental conditions ................................ 34
   2.5  Notation for partial derivatives ....................... 37
   2.6  Use of various derivatives ............................. 38
   2.7  Comparison between Сv and Cp ........................... 40
   2.8  Change of independent variables ........................ 41
   2.9  Maxwell relations ...................................... 43
3  Systems with variable composition ........................... 45
   3.1  Chemical potential ..................................... 45
   3.2  Molar and integral quantities .......................... 46
   3.3  More about characteristic state functions .............. 48
   3.4  Additivity of extensive quantities. Free energy and 
        exergy ................................................. 51
   3.5  Various forms of the combined law ...................... 52
   3.6  Calculation of equilibrium ............................. 54
   3.7  Evaluation of the driving force ........................ 56
   3.8  Driving force for molecular reactions .................. 58
   3.9  Evaluation of integrated driving force as function of
        TorP ................................................... 59
   3.10 Effective driving force ................................ 60
4  Practical handling of multicomponent systems ................ 63
   4.1  Partial quantities ..................................... 63
   4.2  Relations for partial quantities ....................... 65
   4.3  Alternative variables for composition .................. 67
   4.4  The lever rule ......................................... 70
   4.5  The tie-line rule ...................................... 71
   4.6  Different sets of components ........................... 74
   4.7  Constitution and constituents .......................... 75
   4.8  Chemical potentials in a phase with sublattices ........ 77
5  Thermodynamics of processes ................................. 80
   5.1  Thermodynamic treatment of kinetics of internal
        processes .............................................. 80
   5.2  Transformation of the set of processes ................. 83
   5.3  Alternative methods of transformation .................. 85
   5.4  Basic thermodynamic considerations for processes ....... 89
   5.5  Homogeneous chemical reactions ......................... 92
   5.6  Transport processes in discontinuous systems ........... 95
   5.7  Transport processes in continuous systems .............. 98
   5.8  Substitutional diffusion .............................. 101
   5.9  Onsager's extremum principle .......................... 104
6  Stability .................................................. 108
   6.1  Introduction .......................................... 108
   6.2  Some necessary conditions of stability ................ 110
   6.3  Sufficient conditions of stability .................... 113
   6.4  Summary of stability conditions ....................... 115
   6.5  Limit of stability .................................... 116
   6.6  Limit of stability against fluctuations in 
        composition ........................................... 117
   6.7  Chemical capacitance .................................. 120
   6.8  Limit of stability against fluctuations of internal 
        variables ............................................. 121
   6.9  Le Chatelier's principle .............................. 123
7  Applications of molar Gibbs energy diagrams ................ 126
   7.1  Molar Gibbs energy diagrams for binary systems ........ 126
   7.2  Instability of binary solutions ....................... 131
   7.3  Illustration of the Gibbs-Duhem relation .............. 132
   7.4  Two-phase equilibria in binary systems ................ 135
   7.5  Allotropic phase boundaries ........................... 137
   7.6  Effect of a pressure difference on a two-phase
        equilibrium ........................................... 138
   7.7  Driving force for the formation of a new phase ........ 142
   7.8  Partitionless transformation under local equilibrium .. 144
   7.9  Activation energy for a fluctuation ................... 147
   7.10 Ternary systems ....................................... 149
   7.11 Solubility product .................................... 151
8  Phase equilibria and potential phase diagrams .............. 155
   8.1  Gibbs'phase rule ...................................... 155
   8.2  Fundamental property diagram .......................... 157
   8.3  Topology of potential phase diagrams .................. 162
   8.4  Potential phase diagrams in binary and multinary 
        systems ............................................... 166
   8.5  Sections of potential phase diagrams .................. 168
   8.6  Binary systems ........................................ 170
   8.7  Ternary systems ....................................... 173
   8.8  Direction of phase fields in potential phase
        diagrams .............................................. 177
   8.9  Extremum in temperature and pressure .................. 181
9  Molar phase diagrams ....................................... 185
   9.1  Molar axes ............................................ 185
   9.2  Sets of conjugate pairs containing molar variables .... 189
   9.3  Phase boundaries ...................................... 193
   9.4  Sections of molar phase diagrams ...................... 195
   9.5  Schreinemakers' rule .................................. 197
   9.6  Topology of sectioned molar diagrams .................. 201
10 Projected and mixed phase diagrams ......................... 205
   10.1 Schreinemakers' projection of potential phase 
        diagrams .............................................. 205
   10.2 The phase field rule and projected diagrams ........... 208
   10.3 Relation between molar diagrams and Schreinemakers'
        projected diagrams .................................... 212
   10.4 Coincidence of projected surfaces ..................... 215
   10.5 Projection of higher-order invariant equilibria ....... 217
   10.6 The phase field rule and mixed diagrams ............... 220
   10.7 Selection of axes in mixed diagrams ................... 223
   10.8 Konovalov's rule ...................................... 226
   10.9 General rule for singular equilibria .................. 229
11 Direction of phase boundaries .............................. 233
   11.1 Use of distribution coefficient ....................... 233
   11.2 Calculation of allotropic phase boundaries ............ 235
   11.3 Variation of a chemical potential in a two-phase
        field ................................................. 238
   11.4 Direction of phase boundaries ......................... 240
   11.5 Congruent melting points .............................. 244
   11.6 Vertical phase boundaries ............................. 248
   11.7 Slope of phase boundaries in isothermal sections ...... 249
   11.8 The effect of a pressure difference between two
        phases ................................................ 251
12 Sharp and gradual phase transformations .................... 253
   12.1 Experimental conditions ............................... 253
   12.2 Characterization of phase transformations ............. 255
   12.3 Microstructural character ............................. 259
   12.4 Phase transformations in alloys ....................... 261
   12.5 Classification of sharp phase transformations ......... 262
   12.6 Applications of Schreinemakers'projection ............. 266
   12.7 Scheil's reaction diagram ............................. 270
   12.8 Gradual phase transformations at fixed composition .... 272
   12.9 Phase transformations controlled by a chemical
        potential ............................................. 275
13 Transformations in closed systems .......................... 279
   13.1 The phase field rule at constant composition .......... 279
   13.2 Reaction coefficients in sharp transformations
        for p = с + 1 ......................................... 280
   13.3 Graphical evaluation of reaction coefficients ......... 283
   13.4 Reaction coefficients in gradual transformations
        for p = с ............................................. 285
   13.5 Driving force for sharp phase transformations ......... 287
   13.6 Driving force under constant chemical potential ....... 291
   13.7 Reaction coefficients at constant chemical potential .. 294
   13.8 Compositional degeneracies for p = с .................. 295
   13.9 Effect of two compositional degeneracies for p =
        с — 1 ................................................. 299
14 Partitionless transformations .............................. 302
   14.1 Deviation from local equilibrium ...................... 302
   14.2 Adiabatic phase transformation ........................ 303
   14.3 Quasi-adiabatic phase transformation .................. 305
   14.4 Partitionless transformations in binary system ........ 308
   14.5 Partial chemical equilibrium .......................... 311
   14.6 Transformations in steel under quasi-paraequilibrium .. 315
   14.7 Transformations in steel under partitioning of 
        alloying elements ..................................... 319
15 Limit of stability and critical phenomena .................. 322
   15.1 Transformations and transitions ....................... 322
   15.2 Order-disorder transitions ............................ 325
   15.3 Miscibility gaps ...................................... 330
   15.4 Spinodal decomposition ................................ 334
   15.5 Tri-critical points ................................... 338
16 Interfaces ................................................. 344
   16.1 Surface energy and surface stress ..................... 344
   16.2 Phase equilibrium at curved interfaces ................ 345
   16.3 Phase equilibrium at fluid/fluid interfaces ........... 346
   16.4 Size stability for spherical inclusions ............... 350
   16.5 Nucleation ............................................ 351
   16.6 Phase equilibrium at crystal/fluid interface .......... 353
   16.7 Equilibrium at curved interfaces with regard to 
        composition ........................................... 356
   16.8 Equilibrium for crystalline inclusions with regard
        to composition ........................................ 359
   16.9 Surface segregation ................................... 361
   16.10 Coherency within a phase ............................. 363
   16.11 Coherency between two phases ......................... 366
   16.12 Solute drag .......................................... 371
17 Kinetics of transport processes ............................ 377
   17.1 Thermal activation .................................... 377
   17.2 Diffusion coefficients ................................ 381
   17.3 Stationary states for transport processes ............. 384
   17.4 Local volume change ................................... 388
   17.5 Composition of material crossing an interface ......... 390
   17.6 Mechanisms of interface migration ..................... 391
   17.7 Balance of forces and dissipation ..................... 396
18 Methods of modelling ....................................... 400
   18.1 General principles .................................... 400
   18.2 Choice of characteristic state function ............... 401
   18.3 Reference states ...................................... 402
   18.4 Representation of Gibbs energy of formation ........... 405
   18.5 Use of power series in T .............................. 407
   18.6 Representation of pressure dependence ................. 408
   18.7 Application of physical models ........................ 410
   18.1 Ideal gas ............................................. 411
   18.9 Real gases ............................................ 412
   18.10 Mixtures of gas species .............................. 415
   18.11 Black-body radiation ................................. 417
   18.12 Electron gas ......................................... 418
19 Modelling of disorder ...................................... 420
   19.1 Introduction .......................................... 420
   19.2 Thermal vacancies in a crystal ........................ 420
   19.3 Topological disorder .................................. 423
   19.4 Heat capacity due to thermal vibrations ............... 425
   19.5 Magnetic contribution to thermodynamic properties ..... 429
   19.6 A simple physical model for the magnetic 
        contribution .......................................... 431
   19.7 Random mixture of atoms ............................... 434
   19.8 Restricted random mixture ............................. 436
   19.9 Crystals with stoichiometric vacancies ................ 437
   19.10 Interstitial solutions ............................... 439
20 Mathematical modelling of solution phases .................. 441
   20.1 Ideal solution ........................................ 441
   20.2 Mixing quantities ..................................... 443
   20.3 Excess quantities ..................................... 444
   20.4 Empirical approach to substitutional solutions ........ 445
   20.5 Real solutions ........................................ 448
   20.6 Applications of the Gibbs-Duhem relation .............. 452
   20.7 Dilute solution approximations ........................ 454
   20.8 Predictions for solutions in higher-order systems ..... 456
   20.9 Numerical methods of predictions for higher-order
        systems ............................................... 458
21 Solution phases with sublattices ........................... 460
   21.1 Sublattice solution phases ............................ 460
   21.-2 Interstitial solutions ............................... 462
   21.3 Reciprocal solution phases ............................ 464
   21.4 Combination of interstitial and substitutional
        solution .............................................. 468
   21.5 Phases with variable order ............................ 469
   21.6 Ionic solid solutions ................................. 472
22 Physical solution models ................................... 476
   22.1 Concept of nearest-neighbour bond energies ............ 476
   22.2 Random mixing model for a substitutional solution ..... 478
   22.3 Deviation from random distribution .................... 479
   22.4 Short-range order ..................................... 482
   22.5 Long-range order ...................................... 484
   22.6 Long- and short-range order ........................... 486
   22.7 The compound energy formalism with short-range order .. 488
   22.8 Interstitial ordering ................................. 490
   22.9 Composition dependence of physical effects ............ 493
   
   References ................................................. 496
   Index ...................................................... 499

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